Unified Bernoulli-Euler polynomials of Apostol type

Hacène Belbachir (), Yahia Djemmada and Slimane Hadj-Brahim ()
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Hacène Belbachir: RECITS Laboratory
Yahia Djemmada: RECITS Laboratory
Slimane Hadj-Brahim: RECITS Laboratory

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 76-83

Abstract: Abstract The object of this paper is to introduce and study the properties of unified Apostol-Bernoulli and Apostol-Euler polynomials noted by $$\left\{ \mathfrak {V_{n}}(x;\lambda ;\mu )\right\} _{n \ge 0}$$ V n ( x ; λ ; μ ) n ≥ 0 . We study some arithmetic properties of $$\left\{ \mathfrak {V_{n}}(x;\lambda ;\mu )\right\} _{n \ge 0}$$ V n ( x ; λ ; μ ) n ≥ 0 as their connection to Apostol-Euler polynomials and Apostol-Bernoulli polynomials. Also, we give derivation and integration representations of $$\left\{ \mathfrak {V_{n}}(x;\lambda ;\mu )\right\} _{n \ge 0}$$ V n ( x ; λ ; μ ) n ≥ 0 . Finally, we use the umbral calculus approach to deduce symmetric identities.

Keywords: Euler polynomials; Bernoulli polynomials; Apostol-Bernoulli and Apostol-Euler polynomials; generating function; 11B68; 11B83; 11C08; 11C20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00232-x

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